Question

Suppose that a stock pays a dividend of P10 on the first year and increases by 10% per year thereafter until the fifth year. The discount rate is 12 percent. In this case, what is the price of the stock today?

Answer 1

Share price today is the present value of its dividend and the terminal value at the end of 5th year.For this purpose we have to calculate the dividend for each till 6th year.

Share price can be calculated using dividend discount model-

D1=P 10

D2=D1(1+0.10)=11

D3=D2(1+growth rate)=11(1+0.10)=12.10

D4=D3(1+growth rate)=12.10(1+0.10)=13.31

D5=D4(1+growth rate)=13.31(1+0.10)=14.641

It is assumed that,dividend after 5th year is constant.Thus dividend for 6th year is P14.641

Terminal value(Price of stock at the end of 5th year)=D6/(Discount rate-Growth rate)

=14.641/12%-0%

=P 122.01

Now,we have to calculate the present value of dividends till 5th year and terminal value as follow;

=10/(1+0.12)^1+11/(1+0.12)^2+12.10/(1+0.12)^3+13.31/(1+0.12)^4+14.641/(1+0.12)^5+122.01/(1+0.12)^5

=P 112.31

Thus,Price of the stock today is P 112.31